Let \(\alpha \) be a topological automorphism on a locally compact abelian group G, satisfies \(\alpha (p^{2})=p\) for all \(p\in G\). This paper deals with defining Fourier–Wigner, Wigner and Weyl transforms with respect to \(\alpha \), and among other things, it shows that Weyl transform has the same effect as Hilbert–Schmidt operators and the product of two wavelet multipliers.

中文翻译：

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Weyl变换和局部紧阿贝尔拓扑群上两个小波乘子算子的乘积

令\（\ alpha \）为局部紧的阿贝尔群G的拓扑自同构，对于所有\（p \ in G \）满足\（\ alpha（p ^ {2}）= p \）。本文涉及针对\（\ alpha \）定义Fourier–Wigner，Wigner和Weyl变换，并且除其他外，它表明Weyl变换与Hilbert-Schmidt算子以及两个小波乘数的乘积具有相同的作用。